215edo: Difference between revisions

Revision as of 08:24, 3 April 2024

The equal temperament tempers out 4000/3969 and 65625/65536, and the patent val provides the optimal patent val for the 53 & 162 temperament (ditonic extension) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out 2401/2400, 5120/5103, and supports hemififths.

Approximation of odd harmonics in 215edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+1.30	-1.20	+2.34	+2.60	+1.24	+2.26	+0.10	+1.09	-1.70	-1.94	+2.42
Error	Relative (%)	+23.3	-21.5	+41.9	+46.6	+22.2	+40.5	+1.9	+19.5	-30.4	-34.8	+43.4
Steps (reduced)		341 (126)	499 (69)	604 (174)	682 (37)	744 (99)	796 (151)	840 (195)	879 (19)	913 (53)	944 (84)	973 (113)

Since 215 factors into 5 × 43, 215edo contains 5edo and 43edo as its subsets.

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 {{Infobox ET}}
-The '''215 equal temperament''' divides the octave into 215 equal parts of 5.581 cents each. It tempers out 4000/3969 and 65625/65536, and the patent val provides the [[Optimal_patent_val|optimal patent val]] for the 3&amp;53 temperament tempering them both out, and the rank three temperament tempering 4000/3969 out. The 215c val tempers out 2401/2400, 5120/5103, and [[support]]s [[Breedsmic_temperaments#Hemififths|hemififths]] temperament.
+{{EDO intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+The equal temperament [[tempering out|tempers out]] [[4000/3969]] and [[65625/65536]], and the [[patent val]] provides the [[optimal patent val]] for the 53 & 162 temperament ([[ditonic|ditonic extension]]) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out [[2401/2400]], [[5120/5103]], and [[support]]s [[hemififths]].
+=== Odd harmonics ===
+{{Harmonics in equal|215}}
+=== Subsets and supersets ===
+Since 215 factors into {{factorization|215}}, 215edo contains [[5edo]] and [[43edo]] as its subsets.
+[[Category:Ditonic]]
+[[Category:Octagar]]